Where :
11
r = index reliability
k = number of item
2 b
σ
∑ = item variance
2 t
σ
= total variance Meanwhile, in order to find out the variance of each item, the formula is:
Then, the formula to calculate the total variance is:
Having obtained the t-value, each number of items is then checked by critical value of t-table. If the t-value is bigger than t-table, the test is said to be
reliable.
3.6.2.3 Difficulty Level
The difficulty level of test shows how easy, sustain, or difficult the item is. If the index of difficulty is high, an item is considered as an easy item, or vice versa. It
is indicated by the percentage of the students who get the items right. In this N
N Y
Y
2 2
2
∑ −
∑ =
t
σ N
N X
X
2 2
2
∑ −
∑ =
b
σ
study, it is proved by the students’ score of each item maximum score. In order to compute difficulty level, the formula used is :
In which, P = item difficulty
B = the number of students who answer the item correctly JS = the number of students
Table 3.3 The Criteria of Difficulty of the Test
Interval of Difficulty Level Criteria
0.00 P
0.30 Difficult 0.30
P 0.70 Medium
0.70 P
1.00 Easy
3.6.2.4 Discriminating Power
Harris 1969:106 states that the discriminating power is “a measure of the effectiveness of an item discriminating between high and low scores of the whole
test.” In addition, Heaton 1974:173 also views that “the discrimination index of an item indicates the extent to which the item discriminates between testers,
separating the more able testers from the less able.” Discriminating power will measure how well the test items arranged to
identify the differences in the students’ competence. In order to find out the
discriminating power of each item of the scoring system in this study, the following steps were done:
1 Arranging the score of the students in rank order from the highest
score to the lowest. 2
Classifying the students into two groups, namely the upper group and the lower one. The upper group is the students having high
score, while the lower group is the students having low scores. The number of students in both groups should be the same.
3 Counting the number of the upper group students who did the aspect
items of writing correctly. Then, the number of students in the lower group who did the aspect items of writing incorrectly was counted.
4 Computing discriminating power by using the following formula:
t =
Where: t
: Item discrimination
MH :
Mean for upper group ML
: Mean for lower group
∑
2 1
X :
The sum of deviation scores for upper group
∑
2 2
X :
The sum of deviation score for lower group n
1
: The number of students for upper or lower group 27xN
N : The number of students taking the test
⎪⎭ ⎪
⎬ ⎫
⎪⎩ ⎪
⎨ ⎧
− +
−
∑ ∑
1
2 2
2 1
i i
n n
X X
ML MH
The t value then was compared by the t table. If the t value is higher than the t table, so the test could be categorized significantly discriminate the students.
3.6.3 Pre-Test
